Problem: Solve for $x$ and $y$ using elimination. ${5x+y = 32}$ ${2x-y = 10}$
Answer: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $y$ and $-y$ cancel out. $7x = 42$ $\dfrac{7x}{{7}} = \dfrac{42}{{7}}$ ${x = 6}$ Now that you know ${x = 6}$ , plug it back into $\thinspace {5x+y = 32}\thinspace$ to find $y$ ${5}{(6)}{ + y = 32}$ $30+y = 32$ $30{-30} + y = 32{-30}$ ${y = 2}$ You can also plug ${x = 6}$ into $\thinspace {2x-y = 10}\thinspace$ and get the same answer for $y$ : ${2}{(6)}{ - y = 10}$ ${y = 2}$